Spreading Bandwidth

The bandwidth of 1.25 MHz is a compromise between multipath mitigation, receiver complexity, and receiver performance. Larger rates would require more Rake correlators in order to utilize a large fraction of the multipath energy, while smaller rates would suffer from an increased likelihood of so-called "flat fading" and adverse "law of large numbers" effects.

That is, because there would be fewer users on each CDMA channel, the relative power fluctuations, which are proportional to N^-1/2, N=number of users, would be larger. More operating margin is thus needed for stable operation, entailing a penalty in capacity per megahertz.

Multipath delay spreads in urban areas are typically in the range of 2-3 microseconds. Spreading bandwidths significantly larger than 1 MHz would resolve many more multipath components. While there would be less likelihood of fading of each correlator output, there would have to be more of them. The fraction of the energy in each would be smaller, making time and frequency tracking more difficult. Also the search function would have to find smaller signal components, which would require more integration time and therefore degrade performance.

Smaller bandwidths suffer from two problems. First, they would tend to not resolve common multipath situations. In this case, the fading behavior would be very similar to the narrowband systems, exhibiting the so-called flat Rayleigh fading. While some interference averaging might take place, the overall performance would be adversely affected by the more severe fading.

A second consequence of too narrow a bandwidth is that too few users would be serviced by each carrier. If fewer users are present the law-of-large numbers averaging that takes place would be less effective in reducing power fluctuations. The fluctuations in the sum of N random variables, such as the single-user power, are proportional to N^-1/2. With larger fluctuations, more operating margin on the system operating point is needed. The capacity per MHz would be poorer because each CDMA channel would be operating a smaller loading than would be possible with a large bandwidth and a larger user population.

A spreading rate about 2-3 times the reciprocal delay spread is large enough that 2 -3 correlators in a Rake receiver will collect nearly all signal energy, on average. Also, some statistical independence of fading in the correlator outputs can be expected.

Another consideration is the rollout of CDMA system into the existing AMPS infrastructure. 1.25 MHz is 1/8 of the original 10 MHz allocations. The relatively small bandwidth permits an operator to replace about 15% of his AMPS channels with one CDMA channel. But that one CDMA channel has many times the capacity of the AMPS channels it replaced. This permits graceful, gradual, introduction of CDMA into the system.

And finally, after taking into account the frequency allocations for cellular in North America, in which one of the band segments is only 1.5 MHz wide, the choice of 1.25 MHz is seen to be a suitable compromise among all these conflicting considerations.

For more details, see Optimum Bandwidth.

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